The above equality also shows that if AFI is constant, as in some poultry feeding, the daily cost will be minimum when AF$, the as fed price of the ration, is minimum. By Equation (2), the as fed price of the ration is AF$ = C / AF# = 4.3334 $/lb.Īssuming DMI is constant, the cost of feeding one cow for one day will be minimum when DM$, the dry matter price of the ration, is minimum.
The weight of the above ration is AF# = 33.33 lb + 66.67 lb = 100 lb, and the cost is C = (3.00 $/lb) (See books on business mathematics for details.) The coefficients of the X’s are then placed in a matrix and a solution is found by a The last two inequalities are nutrient restrictions or nutrientĬonstraints and say that the ration must have at least 7% protein and at most 8% protein on an asįed basis.
Inequality, called a feed restriction or feed constraint that says at least 50 of these 100 pounds TheĮquality says that the ration must have exactly 100 pounds of as fed weight, followed by an The function Z, called the objective function, is the feed cost that is to be minimized. Linear programming method assumes that the solution is Xa pounds of Feed A, Xb pounds ofįeed B, and Xc pounds of Feed C, where initially Xa, Xb and Xc are unknown as fed weights, Linear programming can also be used to solve multiple feed-mix problems whenįeed inventory is limited, and to optimize feed properties other than cost. Practical feed-mix problems are so large that only computers can solve them.įeed mix problems are solved by a mathematical technique called linear programming, whichĬan be used to restrict feeds, nutrients, ratios of feeds and ratios of nutrients on an as fed or dry Problems have ten to twenty feeds and ten to twenty nutrients with minimum or maximum This problem, whose solution (33.33 lb of Feed AĪnd 66.67 lb of Feed B) is difficult to guess, is a simple feed-mix problem. Other balanced ration has a smaller feed cost. Ration if it satisfies the feed and nutrient restrictions, and is a least-cost balanced ration if no These three feeds that satisfy these feed and nutrient restrictions. Protein, at least 50% of Feed B, and is not more expensive than any other 100-pound mixture of
A feed-mix problem is to find a 100-pound mixture of these feeds that has between 7% and 8%
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